Your duties to protect the health and safety of people affected by your work will not change with Brexit.
You should continue to manage risk in your business in a proportionate way.
The HSE have made minor amendments to regulations to remove EU references but legal requirements will remain the same as they are now. Health and safety standards will be maintained.
The HSE have produced guidance to help you prepare in the event the UK leaves the EU without a deal (and therefore without an implementation period) www.hse.gov.uk/brexit/brexit-no-deal-guidance.htm
Guidance on areas relating to workplace health and safety is also available on GOV.UK